Method and arrangement for reducing feedback data in a MIMO communication system

ABSTRACT

The present invention relates to a method and arrangement for reducing feedback data in a communication system, said communication system comprising a number of transmitter antennas, n τ , and a number of receiver antennas, n R , for parallel spatially independent transmission and reception of signals, wherein a channel response is represented by a matrix (G) containing n R ×n τ  complex variables. The method comprises the steps of: decomposing an expression of said channel response matrix (G) into products of a unitary transform (V), n R ×n T  diagonal matrix (Λ) and a conjugate transpose of a unitary matrix (W). Choosing said unitary matrix (W) such that its diagonal elements are real, substituting said channel response matrix (G) with a representative subset of elements in said decomposed expression of said channel response matrix (G), said representative subset comprising diagonal of a first matrix (Λ) and lower triangle of a second matrix (W) excluding the diagonal.

TECHNICAL FIELD

The present invention relates to a method and arrangement for reducingfeedback data in a communication system. In particular, the presentinvention relates to a method and arrangement for reducing datafeedback, especially channel response, in a Multiple-inputMultiple-Output (MIMO) system.

BACKGROUND OF THE INVENTION

The existing wireless mobile communication systems provide several typesof services and mostly depend on channel coding to overcome anyinferiority of channels. However, due to the increasing demands, forexample for a high-quality multimedia services, in which users cancommunicate with anyone regardless of time and place, the existingservices have evolving into data-oriented services. Accordingly, thereis a high demand for next generation wireless transmission technologyfor transmitting the larger amount of data at a lower error rate. Inparticular, it is very important to transmit data at a high rate in alink in which the amount of required data is large.

For the next generation wireless communication, various antenna systemshave been proposed. For example, a Multiple-input multiple-output (MIMO)system increases spectrum efficiency through all of transmissionantennas without excessive use of a frequency bandwidth. Generally, MIMOis classified into Space-Time Coding (STC), Diversity, Beam Forming(BF), and Spatial Multiplexing (SM) according to the transmissionstructure and scheme of a transmitter, all of which provide high datarate and reliability.

A MIMO system adopts multiple antennas or array antenna totransmit/receive data in the transmitter and receiver. Multiple antennasare provided in different spatial positions, with different fadingfeatures, thus the received signals of adjacent antennas can beapproximated as uncorrelated entirely as long as the spacing betweenadjacent antennas for transmitting/receiving signals in the MIMO systemis large enough. The MIMO system takes full advantage of the spatialcharacteristics of multipath for implementing space diversitytransmission and reception.

FIG. 1 illustrates an exemplary and simplified MIMO system 100constructed by M Tx antennas 103 and N Rx antennas 104. As mentionedearlier, the antenna spacing between the Tx antennas and Rx antennas inthe MIMO system in FIG. 1 is generally big enough, to guarantee thespatial un-correlation of signals. As FIG. 1 shows, in the transmitter,MIMO architecture unit 101 first transforms a channel of data streaminto M channels of parallel sub data streams; then, multiple accesstransform unit 102 performs multiplex processing; finally, thecorresponding M Tx antennas 103 transmit the signal simultaneously intothe wireless channels. The MIMO architecture unit 101 can adopt any oneof the MIMO processing methods, such as STTC (Space Time Trellis Code),space-time block code, space-time Turbo code, BLAST code and etc. Whilemultiple access transform unit 102 can implement TDD, FDD or CDMA.

At the receiver site N Rx 104 antennas receive the broadcasted signals,which are transformed by multiple access inverse transform unit 105,performing multiple access demultiplexing processing, and provided to aMIMO detection unit 106.

Usually, a MIMO antenna system with n_(R) receive and n_(T) transmitantennas operating in a frequency non-selective channel is described bythe following matrix representation:y=Gx+z  (1)

Wherein y is the n_(R)×1 received signal vector, G is the n_(R)×n_(T)MIMO channel response, z is the independent and identically distributedelements Additive White Gaussian Noise (AWGN) at the receiver withindividual variance of σ² _(z) and x is the n_(T)×1 transmitted signalvector with a certain power constraint.

The best performance of such a system is achieved when the channelresponse is known to the transmitter so that the transmit signals can bedesigned accordingly. This is disclosed, for example in G. G Raleigh &J. M. Cioffi, “Spatio-temporal Coding For Wireless Communication” IEEEtrans. On Comm. Vol. 46, no. 3 Mar. 1998, pp. 357-366, and K. C. Zangiand L. G Krasny “Capacity achieving Transmitter and Receiver Pairs forMISO Channels” IEEE Transaction on Wireless Communications Vol. 2 No. 6Nov. 2003, pp 1204-1216.

In many cases, the channel response is only known to the receiverthrough the reference signals sent by the transmitter on a forward linkand therefore requires being explicitly fed back to the transmitter on areverse link. Such a feedback may sometimes be a significant overheadespecially for a configuration with a large number of antennas. It mayalso require a substantial amount of computational power.

Conventionally, the entire channel matrix G is fed back from thereceiver. For the case of two transmit antennas and one receiverantenna, for example, the close-loop mode in 3^(rd) Generation ProjectPlan (3GPP) feeds back one phase factor optimized for the frequencyselective channel to adjust one of the transmitter antennas.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a methodand an arrangement in a MIMO antenna system that reduces feedbackoverhead. Thus, one problem solved by the present invention is to extenda simple solution to the complex MIMO.

Moreover, the present invention extends and generalises the close-loopmode concept in 3GPP and similar concepts to any number of transmit andreceive antennas and also to channels with much greater frequencyselectivity.

These objects are achieved using a method for reducing amount of data ina transmission in a communication system. The communication systemcomprises a number of transmitter antennas, n_(T), and a number ofreceiver antennas, n_(R), for parallel spatially independenttransmission and reception of signals. A channel response is representedby a matrix containing n_(R)×n_(T) complex variables. The inventioncomprises substituting the channel response matrix with a representativesubset of elements in the decomposed expression of the channel responsematrix, in the data transmission.

A method of reducing feedback data in a communication system, thecommunication In more detail, the method of the invention comprises thesteps of: decomposing an expression of the channel response matrix intoproducts of a unitary transform, n_(R)×n_(T) diagonal matrix and aconjugate transpose of a unitary matrix, choosing the unitary matrixsuch that its diagonal elements are real, substituting the channelresponse matrix with a representative subset of elements in thedecomposed expression of the channel response matrix. The representativesubset comprising diagonal of a first matrix and lower triangle of asecond matrix excluding the diagonal. Preferably, the first matrix isn_(R)×n_(R) non-trivial truncation of the n_(R)×n_(T) diagonal matrix,and the second matrix is n_(T)×n_(R) non-trivial truncation of thecorresponding n_(T)×n_(T) unitary matrix. The second matrix isrepresented by:

$\overset{\sim}{W} = \begin{pmatrix}w_{1,1} & \ldots & w_{1,n_{R}} \\\vdots & \ddots & \vdots \\w_{n_{T},1} & \ldots & w_{n_{T},n_{R}}\end{pmatrix}$

According to one embodiment of the invention, the second matrix issolved by choosing a solution and rotating the phase of each column inthe matrix such that the diagonal elements become real. Thus, the secondmatrix is restored from its lower triangle by:

-   -   solving <w₁, w₁>=1 for w_(1,1),    -   solving <w₁, w₂>=0 and <w₂, w₂>=0 for w_(1,2) and w_(2,2), and    -   continuing restoration process until all columns are restored.

Preferably, <w₁, w₁>=1 for w_(1,1) is determined by solving

$w_{1,1} = {\sqrt{1 - {\sum\limits_{j = 2}^{n_{T}}{w_{j,1}}^{2}}}.}$

Preferably, <w₁, w₂>=0 and <w₂, w₂>=0 is determined by solving:

w₁,w₂

=0

w₂,w₂

=1

The method implies continuing restoration process until all columns arerestored by solving:

⟨w₁, w_(l)⟩ = 0 ⋮ ⟨w_(l − 1), w_(l)⟩ = 0 ⟨w_(l), w_(l)⟩ = 1wherein l is an integer ranging from 1 to n_(R).

Most preferably, one advantage of the invention is that the number ofreal coefficients required for specifying the channel response matrix is2n_(R)n_(T)−n² _(R).

According to one aspect of the invention, the system comprises frequencyselective channels and a frequency range is divided into a number ofconsecutive segments and the number of segments are chosen such that achannel response matrix being a function of a frequency, issubstantially constant and the channel response matrix is thenapproximated in each segment using its mean and substitution of eachsegment. Thus, the system comprises frequency selective channels and acontinuous channel response in a frequency domain is approximated by afinite number of frequency non-selective channels.

Preferably, a receiver end determines and feeds back to a transmit endthe representative subset.

According to another aspect of the invention a method is provided forreducing feedback data in a Multiple-input Multiple-Output (MIMO)communication system. The system comprises at least two transmitterantennas, n_(T), and at least two receiver antennas, n_(R), for parallelspatially independent transmission and reception of signals. A channelresponse is represented by a matrix containing n_(R)×n_(T) complexvariables. The method comprising the steps of: decomposing an expressionof the channel response matrix into products of a unitary transform,n_(R)×n_(T) diagonal matrix and conjugate transpose of a unitary matrix,where the unitary matrix is chosen such that its diagonal elements arereal, substituting the channel response matrix with a representativesubset of elements in the decomposed expression of the channel responsematrix, the representative subset comprising diagonal of a first matrixbeing n_(R)×n_(R) non-trivial truncation of the n_(R)×n_(T) diagonalmatrix and lower triangle of a second matrix being n_(T)×n_(R)non-trivial truncation of the corresponding n_(T)×n_(T) unitary matrixexcluding the diagonal.

According to another aspect of the invention a method is provided for aSingle-Input Single-Output (SISO) communication system, the systemcomprising one transmitter antenna and a receiver antenna fortransmission and reception of signals, wherein a channel response isrepresented by a matrix. The method comprises the steps of: decomposingan expression of the channel response matrix into products of a unitarytransform, a diagonal matrix and Hermitian transpose of a unitarymatrix, where the unitary matrix is chosen such that its diagonalelements are real, substituting the channel response matrix with arepresentative subset of elements in the decomposed expression of thechannel response matrix, the representative subset comprising diagonalof a first matrix being non-trivial truncation of the diagonal matrixand lower triangle of a second matrix being non-trivial truncation ofthe corresponding unitary matrix excluding the diagonal.

The invention also relates to an arrangement in a communication network.The communication network comprises a number of transmitter antennas,n_(T), and a number of receiver antennas, n_(R). Each of the antennasbeing arranged for substantially parallel and spatially independenttransmission and reception of signals, wherein a channel response isrealized as a matrix containing n_(R)×n_(T) complex variables. Thearrangement further comprises a data processing unit for decomposing anexpression of the channel response matrix into products of a unitarytransform, a diagonal matrix and a conjugate transpose of a unitarymatrix, where the unitary matrix is chosen such that its diagonalelements are real and means for substituting and transmitting thechannel response matrix with a representative subset of elements in thedecomposed expression of the channel response matrix, wherein therepresentative subset comprises diagonal of a first matrix and lowertriangle of a second matrix excluding the diagonal. The arrangementfurther comprises means for generating the first matrix as a n_(R)×n_(R)non-trivial truncation of the n_(R)×n_(T) diagonal matrix. Preferably,the arrangement further comprises means for generating the second matrixas a n_(T)×n_(R) non-trivial truncation of the corresponding n_(T)×n_(T)unitary matrix.

The invention also relates to a Multiple-Input Multiple-Output (MIMO)architecture unit in a MIMO system comprising a number of transmitterantennas, n_(T), and a number of receiver antennas, n_(R), each of theantennas being arranged for substantially parallel and spatiallyindependent transmission and reception of signals, wherein a channelresponse is realized as a matrix containing n_(R)×n_(T) complexvariables. The architecture unit further comprises a data processingunit for decomposing an expression of the channel response matrix intoproducts of a unitary transform, a diagonal matrix and a conjugatetranspose of a unitary matrix, where the unitary matrix is chosen suchthat its diagonal elements are real and means for substituting andtransmitting the channel response matrix with a representative subset ofelements in the decomposed expression of the channel response matrix,wherein the representative subset comprises diagonal of a first matrixand lower triangle of a second matrix excluding the diagonal.

The invention also relates to a Single-input Single-Output (SISO)receiver unit in a SISO system comprising a transmitter antenna and areceiver antenna, each of the antennas being arranged for independenttransmission and reception of signals, wherein a channel response isrealized as a matrix containing complex variables. The architecture unitfurther comprises a data processing unit for decomposing an expressionof the channel response matrix into products of a unitary transform, adiagonal matrix and a conjugate transpose of a unitary matrix, where theunitary matrix is chosen such that its diagonal elements are real andmeans for substituting and transmitting the channel response matrix witha representative subset of elements in the decomposed expression of thechannel response matrix, wherein the representative subset comprisesdiagonal of a first matrix and lower triangle of a second matrixexcluding the diagonal.

The invention may be realized as a computer program product for reducingfeedback data in a communication system, the communication systemcomprising a number of transmitter antennas, n_(T), and a number ofreceiver antennas, n_(R), for parallel spatially independenttransmission and reception of signals, wherein a channel response isrepresented by a matrix containing n_(R)×n_(T) complex variables. Thus,the computer program product comprises: an instruction set forreceiving, decomposing and storing an expression of the channel responsematrix, the decomposing comprising a function for producing products ofthe unitary transform, n_(R)×n_(T) diagonal matrix, and a Hermitiantranspose of the unitary matrix, an instruction set for choosing theunitary matrix in such a way that its diagonal elements are real, aninstruction set for producing a representative subset of the elements inthe decomposed expression, which comprises diagonal of n_(R)×n_(R)non-trivial truncation of the n_(R)×n_(T) diagonal matrix and lowertriangle of n_(T)×n_(R) non-trivial truncation of the n_(T)×n_(T)unitary matrix excluding diagonals, and an instruction set forsubstituting the channel response matrix with the representative subsetof the elements in the decomposed expression.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a prior art MIMO system.

FIG. 2 is a block diagram of a schematic system according to the presentinvention,

FIG. 3 illustrates schematically a block diagram for dissecting theoptimal transmit/receive architecture,

FIG. 4 is a schematic view of a communication network implementing thepresent invention,

FIG. 5 is a diagram illustrating loss due to approximation in extensionto frequency selective channel.

FIG. 6 is a block diagram illustrating the components of an programproduct computer according to the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 2 illustrates in a schematic way, a simplified MIMIO system 200having transmitter 210 and receiver 220. Transmitter site comprisesn_(T) transmitter antennas 203 and receiver site comprises n_(R)receiver antennas 204. The transmitter transmits signals s_(T) to thereceiver and the receiver processes and feeds back data signal s_(R)containing the channel response matrix to the transmitter. Signal s_(R)is feedback overhead to enable transmitter to perform an optimaltransmission. The present invention provides a new method to reduce thefeedback overhead.

FIG. 3 illustrates a dissected optimal transmit/receive architecture ofa MIMO system 300. Preferably, the optimal transmit and receivearchitecture of a MIMO system consists of a series of linear transformsthat decompose the MIMO channel into min(n_(R), n_(T)) parallel andindependent spatial channels, as illustrated, in this case forn_(R)≦n_(T) in frequency-selective channel. The unitary transform V atthe receiver is related to the MIMO channel response G through aSingular Value Decompression (SVD) given by

$\begin{matrix}{G = {{V\;\Lambda\; W^{H}} = {{{V\left\lbrack {\overset{\sim}{\Lambda}\; 0} \right\rbrack}\left\lbrack {{\overset{\sim}{W}}_{n_{T}{xn}_{R}}{\overset{\sim}{W}}^{\bot}} \right\rbrack}^{H} = {V\;\overset{\sim}{\Lambda}\;{\overset{\sim}{W}}^{H}}}}} & (2)\end{matrix}$wherein W is the corresponding n_(T)×n_(T) unitary matrix multipliedfrom the right, Λ is an n_(R)×n_(T) diagonal matrix whose diagonalelements {√{square root over (λ₁)}, . . . , √{square root over (λ_(n)_(R) )}} (assuming full rank) are the square roots of the eigenvalues ofGG^(H) and, {tilde over (W)} and {tilde over (Λ)} are their n_(T)×n_(R)and n_(R)×n_(T) non-trivial truncations, respectively. Thus, theexpression of the channel response matrix G is decomposed into theproducts of V, Λ and conjugate or Hermitian transpose of W, and W ischosen such that its diagonal elements are real. The gain √{square rootover (Φ_(m))} of a first stage filter 315 in each transmit data streamcan scale the parallel channel gain according to the desiredoptimization criterion and is generally a function of {tilde over (Λ)}and σ_(z) ². In the case of maximizing the capacity of the channel, forexample, it may be a Water-Filling term.

FIG. 3 also illustrates that the transmitter must have information on{tilde over (W)}, {tilde over (Λ)} and σ_(z) ² to generate the desiredtransmit signal. However, unlike the arbitrary channel matrix G, {tildeover (W)} is part of a unitary matrix with a certain structure that canbe exploited. If {tilde over (W)} is rewritten in column vector form:

$\begin{matrix}{{\overset{\sim}{W} = {\begin{pmatrix}w_{1,1} & \ldots & w_{1,n_{R}} \\\vdots & \ddots & \vdots \\w_{n_{T},1} & \ldots & w_{n_{T},n_{R}}\end{pmatrix} = \left\lbrack {W_{1}W_{2}\mspace{14mu}\ldots\mspace{14mu} W_{n_{R}}} \right\rbrack}},} & (3)\end{matrix}$and note that since W is unitary, its column vectors are orthogonal:

$\begin{matrix}{\left\langle {w_{m},w_{n}} \right\rangle = {{w_{m}^{H} \cdot w_{n}} = {{\sum\limits_{j = 1}^{n_{T}}{w_{j,m}^{*} \cdot w_{j,n}}} = {{\delta\left\lbrack {m - n} \right\rbrack}.}}}} & (4)\end{matrix}$

Without loss of generality, it is assumed that all the elements in w₁are known except w_(1,1). Since the columns of {tilde over (W)} isuniquely determined up to a phase rotation, consequently w_(1,1) can bechosen as real and non-negative such that its solution to <w₁, w₁>=1,and

$\begin{matrix}{{w_{1,1} = \sqrt{1 - {\sum\limits_{j = 2}^{n_{T}}{w_{j,1}}^{2}}}},} & (5)\end{matrix}$is unique. Assuming further, without loss of generality, that w₂ isknown except w_(1,2) and w_(2,2) and that w_(2,2) is chosen to be realand non-negative. Consequently, the two unknowns may be uniquelydetermined by solving the following equations:

w₁,w₂

=0  (6)

w₂,w₂

=1

By continuing this process, it can be shown that the l unknowns{w_(1,l), . . . , w_(l,l)} in w_(l) can be uniquely determined bysolving the equations

$\begin{matrix}{{\left\langle {w_{1},w_{l}} \right\rangle = 0}\vdots{\left\langle {w_{l - 1},w_{l}} \right\rangle = 0}{\left\langle {w_{l},w_{l}} \right\rangle = 1}} & (7)\end{matrix}$

Given that w_(l,l) is real and non-negative. Therefore, the number ofreal numbers required to completely specify {tilde over (W)} is

$\begin{matrix}{{2{\sum\limits_{l = 1}^{n_{R}}\left( {n_{T} - I} \right)}} = {{2\; n_{R}n_{T}} - {{n_{R}\left( {n_{R} + 1} \right)}.}}} & (8)\end{matrix}$

Together with the n_(R) real eigenvalues in {tilde over (Λ)}, thisreduces the number of real coefficients required to specify G from2n_(R)n_(T) to 2n_(R)n_(T)−n² _(R), i.e. for example in the feedbacksignal from the receiver to the transmitter.

Thus, the invention according to one preferred embodiment comprisessending the diagonal of {tilde over (Λ)} and an abbreviated orsimplified {tilde over (W)}, as feedback data from the receiver insteadof sending G, which has n_(R)×n_(T) complex variables.

Decomposing G using Eq. 2 provides a number of solutions for {tilde over(W)}. Accordingly, a solution with real diagonal elements is selected.This is obtained by choosing any solution and rotating the phase of eachcolumn in the matrix such that the diagonal elements become real. Thenonly the lower triangle elements, i.e. elements found only in the lowertriangle of the matrix, excluding the main diagonal (I_(ij)=0 if j<j)are fed back, which are sufficient to restore {tilde over (W)}.

{tilde over (W)} is restored by:

-   -   Solving <w₁, w₁>=1 for w_(1,1), from Eq. (5). The solution        exists and is unique science w_(1,1), is the only unknown.    -   Solving <w₁, w₂>=0 and <w₂, w₂>=0 using Eq. (6) for w_(1,2) and        w_(2,2). The solution exists and is unique as w_(1,1) and        w_(2,2) are the only unknowns.    -   Continuing the process until all columns are restored, by        solving Eq. (7) for the unknowns {w_(1,l), . . . , w_(l,l)},        wherein l=1 to n_(R).

Thus, for the common case of MIMO spatial multiplexing wheren_(R)≈n_(T), the reduction in feedback overhead can be as much asapprox. 50%.

A frequency selective channel is one whose channel response matrix G isa function of the frequency f, or G(f). According to another aspect ofthe present invention, for frequency selective channel equation (1) willbe represented byy(f)=G(f)×(f)+z(f),  (9)and the same approach as mentioned earlier can be applied to across thefrequency. Instead of 2n_(R)n_(T) real functions of f in G(f), thefeedback now consists of 2n_(R)n_(T)−n² _(R) real functions of f. Forexample each element in the MIMO channel frequency response G(f) isFourier transform of a digital filter such as an Finite Impulse Response(FIR) filter, e.g. having L taps.

The present invention is applied to frequency selective channel case isby assuming each entry in the concise representation, as descriedearlier, as a function of frequency instead of scalar, using TransmitDiversity with Constrained Feedback (TDFC) to convert each function to afinite number of taps.

One problem which can occur is to quantify the number of taps requiredto accurately represent the eigenvalues {tilde over (Λ)}(f) and theircorresponding eigenvectors {tilde over (W)}(f). For large number oftransmit antennas, the components in {tilde over (Λ)}(f) are almostflat, and therefore require much less L taps to represent total numberof FIR coefficients, it is possible to apply Transmit Diversity withConstrained Feedback (TDCF) techniques to the elements in {tilde over(Λ)}(f) and {tilde over (W)}(f), see for example L. Krasny and J. Guey,“Transmit Diversity with Constrained Feedback”, 14^(th) IST Mobile &Wireless Communications Summit, Dresden, June 2005. Feedback overheadreduction is still possible as long as the Signal-Noise Ratio (SNR) lossdue to the mismatch is smaller than feeding back the original channelresponse with equal amount of compression.

Alternatively, it is possible to approximate the continuous channelresponse in the frequency domain by a finite number of frequencynon-selective channels and then apply the same principle to eachsub-band. From sample point of view, an impulse response with L-tap canbe represented by L equally spaced sampling points in the frequencydomain. Therefore, dividing the frequency response of the channels intoL sub-bands should be reasonable approximation and the proportion of thereduction in feed-back overhead is the same as the flat fading channel.

Thus, for frequency selective channel, the frequency range is dividedinto L consecutive segments. The number of segments are chosen such thatG(f) is substantially constant. G(f) is then approximated in eachsegment using its mean and the aforementioned frequency non-selectivetechnique is applied to each segment.

FIG. 4 illustrates an embodiment for evaluating the loss in performancedue this quantization process. The system 400 comprises a transmitterbase station 401, four transmit antennas 403 a-403 d and two receiveantennas 404 a and 404 b connected to a user device 405. The transmitterbase station and the user device are provided with a processing unit(not shown) for processing the data in accordance with the presentinvention. Reference signs 4011 to 4013 relate to exemplary processingarrangements in one side of the communication network for processing thematrix.

The system is assumed to operate in for example 3GPP Typical Urban (TU)channel, scaled four times to 20 MHz bandwidth with L=40 taps. Thus thefrequency response of the channel is divided into 40 sub-bands or“chunks” each with a bandwidth of 500 KHz. FIG. 5 illustrates the MIMOchannel's mutual information averaged over a large number ofrealizations. The performance results for the ideal close-loop,open-loop and Single Input Single Output (SISO) are given as references.Between the ideal close-loop and open-loop results, three curves withdifferent degree of approximation are situated. The dashed curvecorresponds to the case where the average (over frequency) of thechannel's frequency response in each chunk is used as its flat fadingapproximation. The loss with respect to the ideal case is very small.Even when the averaging range increases to two and four chunks, markedwith stars and circles respectively, there is still significant gainover the open loop approach.

Although, the invention is described in an exemplary way to systemshaving n_(R)≦n_(T), it will be appreciated by a skilled person that theteachings of the invention may equally be applied to systems havingn_(R)>n_(T).

The method of the invention may be implemented as hardware and/orsoftware. An instruction set 600, as illustrated in FIG. 6, forimplementing the invention in the receiver architecture may comprise:

-   -   Instructions 601 for receiving, decomposing and storing an        expression of the channel response matrix G    -   The decomposing comprising a function 602 for producing products        of the unitary transform V, the n_(R)×n_(T) diagonal matrix, Λ,        and the Hermitian transpose of the unitary matrix, W,    -   Instructions 602 for choosing the unitary matrix in such a way        that its diagonal elements are real,    -   Instructions 603 for producing a representative subset of the        elements in the decomposed expression, which comprise diagonal        of n_(R)×n_(R) non-trivial truncation of said n_(R)×n_(T)        diagonal matrix Λ and lower triangle of n_(T)×n_(R) non-trivial        truncation of the n_(T)×n_(T) unitary matrix, W, excluding the        diagonal    -   Instructions 604 for substituting the channel response matrix G        with the representative subset of the elements in the decomposed        expression.

The invention is not limited to the described and illustratedembodiments; especially the number of transmitters, receivers andantennas may vary.

1. A method of reducing feedback data in a communication system, saidcommunication system comprising a number of transmitter antennas, n_(T),and a number of receiver antennas, n_(R), for parallel spatiallyindependent transmission and reception of signals, wherein a channelresponse is represented by a matrix (G) containing n_(R)×n_(T) complexvariables, the method comprising the steps of: decomposing by a dataprocessing device, an expression of said channel response matrix (G)into products of a unitary transform (V), n_(R)×n_(T) diagonal matrix(Λ) and a conjugate transpose of a unitary matrix (W), choosing saidunitary matrix (W) such that its diagonal elements are real,substituting said channel response matrix (G) with a representativesubset of elements in said decomposed expression of said channelresponse matrix (G), said representative subset comprising diagonalelements of a first matrix ({tilde over (Λ)}) and lower triangleelements of a second matrix ({tilde over (W)}) excluding diagonalelements.
 2. The method of claim 1, wherein said first matrix ({tildeover (Λ)}) is n_(R)×n_(R) non-trivial truncation of said n_(R)×n_(T)diagonal matrix (Λ).
 3. The method of claim 1, wherein said secondmatrix ({tilde over (W)}) is n_(T)×n_(R) non-trivial truncation of saidcorresponding n_(T)×n_(T) unitary matrix (W).
 4. The method according toclaim 1, wherein said second matrix is represented by:$\overset{\sim}{W} = {\begin{pmatrix}w_{1,1} & \ldots & w_{1,n_{R}} \\\vdots & \ddots & \vdots \\w_{n_{R},1} & \ldots & w_{n_{R},n_{R}}\end{pmatrix}.}$
 5. The method of claim 4, wherein said second matrix({tilde over (W)}) is solved by choosing a solution and rotating thephase of each column in the matrix such that the diagonal elementsbecome real.
 6. The method according to claim 5, wherein said secondmatrix ({tilde over (W)}) is restored from its lower triangle by:solving <W₁, W₁>=1 for W_(1,1), solving <W₁, W₂>=0 and <W₂, W₂>=0 forw_(1,2) and w_(2,2), and continuing restoration process until allcolumns are restored.
 7. The method of claim 6, wherein <W₁, W₁>=1 forW_(1,1) is determined by solving$W_{1,1} = \sqrt{1 - {\sum\limits_{j = 2}^{n_{r}}{W_{j,1}}^{2}}}$wherein j is an integer.
 8. The method of claim 6, wherein <W₁, W₂>=0and <W₂, W₂>=0 is determined by solving: (W₁,W₂)=0 (W₂,W₂)=1.
 9. Themethod of claim 6, wherein continuing restoration process until allcolumns are restored by solving: (W₁, W₁) = 0 ⋮(W_(l − 1), W_(l)) = 0(W_(l), W_(l)) = 1 wherein l is an integer ranging from 1 to n_(R). 10.The method according to claim 1, wherein number of real coefficientsrequired to specify said channel response matrix (G) is 2n_(R)n_(T)−n²_(R).
 11. The method according to claim 1, wherein said system comprisesfrequency selective channels and a frequency range is divided into anumber (L) of consecutive segments and the number of segments are chosensuch that a channel response matrix (G(f)) being a function of afrequency (f), is substantially constant and said channel responsematrix is then approximated in each segment using its mean andsubstitution of each segment.
 12. The method according to claim 1,wherein said system comprises frequency selective channels and acontinuous channel response in a frequency domain is approximated by afinite number of frequency non-selective channels.
 13. The methodaccording to claim 1, wherein a receiver end determines and feeds backto a transmit end said representative subset.
 14. A method of reducingfeedback data in a Multiple-Input Multiple-Output (MIMO) communicationsystem, said system comprising at least two transmitter antennas, n_(T),and at least two receiver antennas, n_(R), for parallel spatiallyindependent transmission and reception of signals, wherein a channelresponse is represented by a matrix (G) containing n_(R)×n_(T) complexvariables, the method comprising the steps of: decomposing by a dataprocessing device, an expression of said channel response matrix (G)into products of a unitary transform (V), n_(R)×n_(T) diagonal matrix(Λ) and conjugate transpose of a unitary matrix (W), where said unitarymatrix (W) is chosen such that its diagonal elements are real,substituting said channel response matrix (G) with a representativesubset of elements in said decomposed expression of said channelresponse matrix (G), said representative subset comprising diagonalelements of a first matrix ({tilde over (Λ)}) being n_(R)×n_(R)non-trivial truncation of said n_(R)×n_(T) diagonal matrix (Λ) and lowertriangle elements of a second matrix ({tilde over (W)}) beingn_(T)×n_(R) non-trivial truncation of said corresponding n_(T)×n_(T)unitary matrix (W) excluding the diagonal elements.
 15. A method ofreducing feedback data in a Single-Input Single-Output (SISO)communication system, said system comprising one transmitter antenna anda receiver antenna for transmission and reception of signals, wherein achannel response is represented by a matrix (G), the method comprisingthe steps of: decomposing by a data processing device, an expression ofsaid channel response matrix (G) into products of a unitary transform(V), a diagonal matrix (Λ) and Hermitian transpose of a unitary matrix(W), where said unitary matrix (W) is chosen such that its diagonalelements are real, substituting said channel response matrix (G) with arepresentative subset of elements in said decomposed expression of saidchannel response matrix (G), said representative subset comprisingdiagonal elements of a first matrix ({tilde over (Λ)}) being non-trivialtruncation of said diagonal matrix (Λ) and lower triangle elements of asecond matrix ({tilde over (W)}) being non-trivial truncation of saidcorresponding unitary matrix (W) excluding diagonal elements.
 16. Anarrangement in a communication network, said communication networkcomprising a number of transmitter antennas, n_(T), and a number ofreceiver antennas, n_(R), each of said antennas being arranged forsubstantially parallel and spatially independent transmission andreception of signals, wherein a channel response is realized as a matrix(G) containing n_(R)×n_(T) complex variables, wherein said arrangementfurther comprises: a data processing device for decomposing anexpression of said channel response matrix (G) into products of aunitary transform (V), a diagonal matrix (Λ) and a conjugate transposeof a unitary matrix (W), where said unitary matrix (W) is chosen suchthat its diagonal elements are real; and means for substituting andtransmitting said channel response matrix (G) with a representativesubset of elements in said decomposed expression of said channelresponse matrix (G)₁ wherein said representative subset comprisesdiagonal elements of a first matrix ({tilde over (Λ)}) and lowertriangle elements of a second matrix ({tilde over (W)}) excludingdiagonal elements.
 17. The arrangement of claim 16, further comprisingmeans for generating said first matrix ({tilde over (Λ)}) as an_(R)×n_(R) non-trivial truncation of said n_(R)×n_(T) diagonal matrix(Λ).
 18. The arrangement of claim 16, further comprising means forgenerating said second matrix ({tilde over (W)}) as a n_(T)×n_(R)non-trivial truncation of said corresponding n_(T)×n_(T) unitary matrix(W).
 19. A Multiple-Input Multiple-Output (MIMO) architecturearrangement in a MIMO system comprising a number of transmitterantennas, n_(T), and a number of receiver antennas, n_(R), each of saidantennas being arranged for substantially parallel and spatiallyindependent transmission and reception of signals, wherein a channelresponse is realized as a matrix (G) containing n_(R)×n_(T) complexvariables, wherein said architecture arrangement further comprises: adata processing device for decomposing an expression of said channelresponse matrix (G) into products of a unitary transform (V), a diagonalmatrix (Λ) and a conjugate transpose of a unitary matrix (W), where saidunitary matrix (W) is chosen such that its diagonal elements are real;and means for substituting and transmitting said channel response matrix(G) with a representative subset of elements in said decomposedexpression of said channel response matrix (G), wherein saidrepresentative subset comprises diagonal elements of a first matrix({tilde over (Λ)}) and lower triangle elements of a second matrix({tilde over (W)}) excluding diagonal elements.
 20. A Single-InputSingle-Output (SISO) receiver arrangement in a SISO system comprising atransmitter antenna and a receiver antenna, each of said antennas beingarranged for independent transmission and reception of signals, whereina channel response is realized as a matrix (G) containing complexvariables, wherein said receiver arrangement further comprises: a dataprocessing device for decomposing an expression of said channel responsematrix (G) into products of a unitary transform (V), a diagonal matrix(Λ) and a conjugate transpose of a unitary matrix (W), where saidunitary matrix (W) is chosen such that its diagonal elements are real;and means for substituting and transmitting said channel response matrix(G) with a representative subset of elements in said decomposedexpression of said channel response matrix (G), wherein saidrepresentative subset comprises diagonal elements of a first matrix({tilde over (Λ)}) and lower triangle elements of a second matrix({tilde over (W)}) excluding diagonal elements.
 21. A non-transitorycomputer program product reducing feedback data in a communicationsystem, said communication system comprising a number of transmitterantennas, n_(T), and a number of receiver antennas, n_(R), for parallelspatially independent transmission and reception of signals, wherein achannel response is represented by a matrix (G) containing n_(R)×n_(T)complex variables, the computer program product comprising: aninstruction set for receiving, decomposing and storing an expression ofthe channel response matrix (G), said decomposing comprising a functionfor producing products of the unitary transform (V), n_(R)×n_(T)diagonal matrix, (Λ), and a Hermitian transpose of the unitary matrix(W), an instruction set for choosing said unitary matrix in such a waythat its diagonal elements are real, an instruction set for producing arepresentative subset of the elements in the decomposed expression,which comprises diagonal elements of n_(R)×n_(R) non-trivial truncationof said n_(R)×n_(T) diagonal matrix (Λ) and lower triangle elements ofn_(T)×n_(R) non-trivial truncation of the n_(T)×n_(T) unitary matrix (W)excluding diagonal elements, and an instruction set for substitutingsaid channel response matrix (G) with said representative subset of theelements in the decomposed expression.